adverbials of place ?

Dear teachers,

When we say that some phrases are objects of a prepostion can they also be adverbials ?

Examples:

a) go up the stairs => stairs is the object of the preposition up; can we also say that "up the stairs" is an adverbial of place?

Same thing for : Wait in the car, Sit on the bed, Walk down the street and Swim across the stream. Are these elements objects of the prepositions they are introduced with AND adverbials of place? 

Many thanks,

Hela  

Hello everybody,

Would it be possible to analyse "He went up the stairs" this way:

he = subject;  went up = verb;  the stairs = direct object     or is it definitely:

he = subject;  went = verb;  up the stairs = adverbial of place ?

All the best,

Hela